Variance & Standard Deviation
How spread out is your data? The two core measures of dispersion
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Explanation
Variance and standard deviation measure how spread out values are from the mean.
Variance — average of squared differences from the mean: `` data = [2, 4, 4, 4, 5, 5, 7, 9], mean = 5 differences²: (2-5)²=9, (4-5)²=1, (4-5)²=1, (4-5)²=1, (5-5)²=0, (5-5)²=0, (7-5)²=4, (9-5)²=16 variance = (9+1+1+1+0+0+4+16) / 8 = 4.0
Standard Deviation — square root of variance (same units as data): `` std = √4.0 = 2.0
Why this matters: A small std means values cluster tightly around the mean. A large std means they are spread far apart. This is critical in ML — features with very different scales need to be normalized.
Population vs Sample: Divide by N for population variance, by (N-1) for sample variance (Bessel's correction).
Examples
NumPy makes this easy
ddof=1 uses N-1 for sample std
import numpy as np
data = [2, 4, 4, 4, 5, 5, 7, 9]
print(np.var(data)) # 4.0 (population)
print(np.std(data)) # 2.0 (population)
print(np.std(data, ddof=1)) # 2.138 (sample)How well did you understand this?
Next in Mathematics for Data Science
What is a Distribution?